# Thread: Finding the relationship between two graphs

1. ## Finding the relationship between two graphs

I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.

2. Originally Posted by katpul
I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.
It's guessing on my side, but:

If two lines $l_1$ and $l_2$ have the slopes $m_1$ and $m_2$ respectively and the slopes have the property:

$m_1 \cdot m_2 = -1$

then the lines are perpendicular to each other:

$m_1 \cdot m_2 = -1~\implies~l_1\ \perp \ l_2$

3. I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.
Look at the slopes of the two lines: -2 and 1/2. Notice anything about these values? They are negative reciprocals of each other. Does that sound familiar? It means that the lines are perpendicular to each other.

4. ## Thank You

Thank you guys. This is one of those things where it is so simple and obivious I just couldn't see it.

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